This is a simple synthetic example taken from [1]} in which the source of the “misspecification” is a poorly chosen prior. Since there is no misspecification in the observation models the interpolating models \({\tilde{p}}^{(k)}_\delta ,\ \delta \ge 0\)  (including Cut and Bayes) concentrate, in the limit \(n\rightarrow \infty \)  with \(m/n\)  constant, on the true parameter values \((\varphi ^*,\theta ^*)\) . The KL-divergence between \(p^*\)  and \({\tilde{p}}^{(k)}_{y,z,\delta }\)  tends to zero and the ELPD converges to a constant \(\int p^*\log (p^*)dydz\)  independent of \(\delta \) .
